Question: $\dfrac{ 2n - 6p }{ -8 } = \dfrac{ -2n - 10q }{ -8 }$ Solve for $n$.
Explanation: Notice that the left- and right- denominators are the same $\dfrac{ 2n - 6p }{ -{8} } = \dfrac{ -2n - 10q }{ -{8} }$ So we can multiply both sides by $-8$ $-{8} \cdot \dfrac{ 2n - 6p }{ -{8} } = -{8} \cdot \dfrac{ -2n - 10q }{ -{8} }$ $2n - 6p = -2n - 10q $ Combine $n$ terms on the left. ${2n} - 6p = -{2n} - 10q$ ${4n} - 6p = -10q$ Move the $p$ term to the right. $4n - {6p} = -10q$ $4n = -10q + {6p}$ Isolate $n$ by dividing both sides by its coefficient. ${4}n = -10q + 6p$ $n = \dfrac{ -10q + 6p }{ {4} }$ All of these terms are divisible by $2$ $n = \dfrac{ -{5}q + {3}p }{ {2} }$